There are a number of applications in which it is desirable to maintain specific beam patterns in satellite-based phased array antennas. For example, in a variety of satellite communications and ranging applications, including various global-positioning-system (“GPS”) applications, it is desirable to maintain a fixed “footprint” on the terrestrial surface, a term sometimes used in the art to refer to the pattern of the beam on the surface. Maintaining a fixed footprint is generally straightforward in cases where the satellite is in a geostationary orbit, but it may be difficult to maintain a fixed footprint in cases where the satellite is in a nongeostationary or elliptical orbit. In such cases, the footprint naturally tends to move over the terrestrial surface as the elevation of the satellite changes, the terrestrial motion of the footprint being a reflection of the spatial orbital motion of the satellite relative to the terrestrial body. Continuous beam shaping is required to maintain a fixed footprint.
The difficulty in maintaining a fixed footprint for satellites in nongeostationary orbits may also be complicated by imposition of a variety of performance criteria. For example, the satellite may be required to provide beams that meet certain power and phase characteristics, particularly in placing limits on sidelobe power outside of a defined service region and transition region. A number of efforts to provide fixed footprints with satellite systems can be commonly characterized by the fact that they are limited to only certain predetermined beam shapes and sizes, such as for fixed-radius circles. These limitations greatly reduce the flexibility that is desired, particularly for applications that may specify a service region having a unique shape and size. Considering the speed at which satellites may travel relative to the Earth, especially in low and mid-Earth orbits, accurately computing a beam pattern for a phased-array antenna that will maintain the desired footprint has proven difficult.
There are currently techniques for synthesizing phased array beam patterns in applications where the desired beam shape does not change significantly in a matter of minutes or even seconds. These techniques, however, are not useful in synthesizing beam patterns in real time or near real time because the computational algorithms they use are too slow and often take tens of minutes to hours to arrive at a solution. One alternative approach to more quickly synthesize phased-array shaped beams has been described in a pending patent application entitled FIXED FOOTPRINT IN NONGEOSTATIONARY SATELLITES by Khalil J. Maalouf et al. filed on Apr. 1, 2004, application Ser. No. 10/816,692, the disclosure of which is incorporated by reference in its entirety. The approach of Maalouf et al., in general terms, relies on iteratively calculating a mini-norm solution to a Taylor series expansion of the conventional far-field gain equations. While effective in many situations, improving the accuracy, convergence and robustness of the approach of Maalouf et al. will only expand the applicability of this type of approach to synthesizing beam patterns in a wider variety of situations.
There is accordingly a general need in the art for improved methods and systems that robustly and accurately provide quick synthesis of shaped phased array antenna beams.